modeling repeating patterns onto a curved surface
Create a Mesh Cylinder and set the number of Vertices to 6, then add a Solidify Modifier.

Then add an Array Modifier with Merge checked

Add a second Array Modifier and set the Constant offset (and Merge)

Add a Curve, here I have added a Bezier Circle, set to non-cyclic, rotated 90 on the X and scaled up.
Add a Curve Modifier to your Cylinder stack and use the new Curve as the Object.

Obviously you can set the curve relevant to your requirements but that shows the basics.